Bicycles are gaining more and more popularity, especially in crowded cities where there is a problem with traffic jams and a limited number of parking spaces. The bicycles are also often used by mountain bikers during riding on off-road trails. In both cases, the important parameters are the stiffness of the bicycle frame, the weight of the bicycle, but also driving comfort. To improve comfort and reduce vibrations in the bicycle frame both front and rear shock absorbers are used. The use of traditional shock absorbers increase the weight of the bike and its price. The work characterizes a modern damping system, Softtail type, designed by AG Motors. In this case, the damping element (elastomer) was placed directly in the rear fork. Analyses of polyurethanes of various hardness were carried out in terms of the possibility of using them as a vibration damper. A numerical and experimental analysis of the bicycle frame was performed, adapted to the a new shock-absorber system. Strength, fatigue and impact tests were carried out in accordance with the relevant bicycle standards. Research has shown that the frame bicycle with the Softtail system, meets the requirements of the standards.